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Simplifying 2a(8a + 6)(8a + 6) = 0 Reorder the terms: 2a(6 + 8a)(8a + 6) = 0 Reorder the terms: 2a(6 + 8a)(6 + 8a) = 0 Multiply (6 + 8a) * (6 + 8a) 2a(6(6 + 8a) + 8a * (6 + 8a)) = 0 2a((6 * 6 + 8a * 6) + 8a * (6 + 8a)) = 0 2a((36 + 48a) + 8a * (6 + 8a)) = 0 2a(36 + 48a + (6 * 8a + 8a * 8a)) = 0 2a(36 + 48a + (48a + 64a2)) = 0 Combine like terms: 48a + 48a = 96a 2a(36 + 96a + 64a2) = 0 (36 * 2a + 96a * 2a + 64a2 * 2a) = 0 (72a + 192a2 + 128a3) = 0 Solving 72a + 192a2 + 128a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '8a'. 8a(9 + 24a + 16a2) = 0 Factor a trinomial. 8a((3 + 4a)(3 + 4a)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75Subproblem 3
Set the factor '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75Solution
a = {0, -0.75, -0.75}
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